New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties

Ortigueira, Manuel D.; Machado, J. A. Tenreiro

http://hdl.handle.net/10400.22/19020

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Autores

Ortigueira, Manuel D.

Machado, J. A. Tenreiro

Resumo(s)

In this paper we introduce new discrete-time derivative concepts based on the bilinear (Tustin) transformation. From the new formulation, we obtain derivatives that exhibit a high degree of similarity with the continuous-time Grünwald-Letnikov derivatives. Their properties are described highlighting one important feature, namely that such derivatives have always long memory.